1. Bellwork~ Simplify 1.) x • x3 2.) 53 • 55 3.) (32)3 4.) (-3x3y2)3
2.) 58
3.) 36 =1029
4.) -27x9y6
5.) 9x2
6.) -3x2

2. Bellwork~ Simplify
Finish Worksheet 8.1 (1-24)

3. Today’s Objective
To be able to apply the exponent rules when the exponent is negative or zero.

4. Exponent Rules 1.) am • an = 2.) (am)n = 3.) (a • b)m 4.) a-n =
3.) am • bm
4.) 1/an
5.) 1

5. A Table of 2’s 24= 23= 22= 21= 20= 16 8 4 2 2-1= 2-2= 2-3= 2-4= 2-5=
Apply the Rule
Describe the pattern
24=
23=
22=
21=
20= 16 8 4 2
2-1=
2-2=
2-3=
2-4=
2-5=
1/21=
1/22=
1/23=
1/24=
1/25=
1/2
1/4
1/8
1/16
1/32 1

6. Find the Pattern
Notice the pattern and complete the table.

7. Negative Exponent 24= 23= 22= 21= 20= 16 8 4 2 1 2-1= 2-2= 2-3= 2-4=
Let’s Look at the table of 2’s
24=
23=
22=
21=
20= 16 8 4 2 1
2-1=
2-2=
2-3=
2-4=
2-5=
1/21=
1/22=
1/23=
1/24=
1/25=
1/2
1/4
1/8
1/16
1/32

8. What’s the least number of times that you can go to McDonald’s?
Negative Exponent
What’s the least number of times that you can go to McDonald’s?

9. Is it possible to go to McDonald’s -1 times?
Negative Exponent
Is it possible to go to McDonald’s -1 times? NO
If we can’t go to McDonalds -1 times, How can we express 2-1 ?

10. Negative Exponent
22 Means… 2 • 2 = So…..
21 Means… 2 = So…..
What does 2-1 Mean?

11. Negative Exponent
What does 2-1 Mean?
You cannot leave an exponent negative because there is no way to express it’s meaning.
2-1 = 1/21 = 1/2

12. In order to maintain the pattern, 2-1 = 1/21 = 1/2
2-1=
2-2=
2-3=
2-4=
2-5=
1/21=
1/22=
1/23=
1/24=
1/25=
1/2
1/4
1/8
1/16
1/32

13. Negative Exponent Examples
1.) 3-2 =
2.) x-3 =
3.) xy-2 =
4.) (xy)-2 =
5.) (23)-2 =
1.) 1/32=1/9
2.) 1/x3
3.) x/y2
4.) 1/(xy)2 =
5.)
Next Slide

14. Negative Exponent
5.) (23)-2 =
Rule # = 1/26 = 1/64
Rule # /(23)2 = 1/26 = 1/64

15. You Try These
1.) 4-2 =
2.) y-2 =
3.) x2y-3 =
4.) (4-1)2 =
5.) 1/4-2 =
1.) 1/42=1/16
2.) 1/y2
3.) x2/y3
4.) 1/42 =1/16
5.) 42 = 16

16. Zero Exponent
Let’s examine: 32 • 3-2 =
1.) 32 • 1/32 = • 1/9 = 1 Now Try Rule #1
2.) = 30 = 1 So…..
Anything0 = 1

17. Zero Exponent
Let’s Examine 72/72
72 = 7 • 7 So…..
72/72 = 7•7 = • Or….
72/72 = 49/49 = 1 Or….

18. Zero Exponent
If we apply Rule #6 to:
Rule #6
72/72 = 72-2 = 70 = 1

19. Zero Exponent
1.) 170 =
2.) (5x)0 =
3.)(4x)0y-3 =
4.) 70 •2-2 =
5.) x-2 • x2 =
1.) 1
2.) 1
3.) 1/y3
4.) 1/4 =
5.) 1

20. Bellwork~ Simplify 1.) x • x-3 2.) 5-3 • 55 3.) (2-2)3 4.) (-3x3y2)3
2.) 52
3.) 1/26
4.) -27x9y6
5.) 9x2
6.) -x2/3

21. Today’s Objective
To be able to apply the exponent rules when when dividing exponents with like bases.

22. Exponent Rules
6.) am an
7.) a n b
6.) am-n
7.) an bn

23. What’s the meaning of...
But what about x x3

24. x2 x5 means x • x • x • x • x x3 means x • x • x So….
What’s the meaning of...
x5 means x • x • x • x • x
x3 means x • x • x
So….
x5 = x • x • x • x • x x3 = x • x • x x2

25. What’s the meaning of...
Explain the exponent rule for dividing with like bases to your `neighbor.

26. 1.) x3 x5 2.) x3 x3 3.) x-3 What’s the meaning of... x3 = 1 x5 x2

27. The Secret ex.#1
Where ever the largest positive exponent is located in the problem is where the exponent will be in the answer. For Example:
x3 x5
Since x5 is on the bottom, the exponent will remain on the bottom in the answer 1/x2 .

28. The Secret ex.#2
Where ever the largest positive exponent is located in the problem is where the exponent will be in the answer. For Example:
x3 x-5
Since x3 is on the top, the exponent will remain on the top in the answer x8 .

29. The Secret ex.#3
Where ever the largest positive exponent is located in the problem is where the exponent will be in the answer. For Example:
x-3 x-5
Since x-3/x-5 = x5/x3 and x5 is on the top, the exponent will remain on the top in the answer x2 .

30. Slates
1.) 43 • 42 =
1.) 45
2.) x6
2.) x2 • x4 =
3.) 8x3
3.) (2x)3 =
4.) 2-3 • 2-2 =
4.) 1/25
5.) 3x-5 =
5.) 3/x5

31. Slates 6.) 1/7x-2 = 6.) x2/7 7.) 8x-3• 1/y-4 8.) 49 8.) 76/74 =
7.) 8y4/x3
7.) 8x-3• 1/y-4
8.) 49
8.) 76/74 =
9.) (4/5)2 =
9.) 16/25
10.) (4/5)-2 =
10.)25 /16

32. Do the special problems worksheet

33. Classwork Do worksheets 8.2-8.3 homework page 409 (2-40 even)

34. Bellwork Simplify 1.) 4xy3 5xy-3 2y x2 2.) 14x3y -2xy -4xy-3 -x
3.) -9x3y7 (2xy) x2y x2y2

35. Bellwork Simplify
1.) 4xy3 5xy y x2
20x x2y y

36. Bellwork Simplify
2.) 14x3y xy xy x
-28x4y x2y-3
-7x2y5

37. Bellwork Simplify = 6xy4 3.) -9x3y7 (2xy)2 x2y3 -6x2y2

38. Then complete the Special Problems worksheet.
Classwork
Then complete the Special Problems worksheet.
Homework Pg 426 (5-22)

39. Special Problems 1.) (8x3)2(¼x2)3 = 82x6 • 1/64x6 x12

40. Bellwork Simplify
3.) -18x3y xy5
2x2 y2

41. Bellwork Simplify 4.) 8x2y-2 (4xy2)-1 x-2y x2y
8x2 • x y2 • y (4xy2)x2y
8x x3y6
= 2x y6

42. Bellwork Simplify
5.) 32xy3 -2xy x3y -4y
-4y x x
-2y x

43. Bellwork Simplify 6.) 5x3y-1 (5x2y)-1 x-2y2 xy-1 5x5 y y3 (5x2y)•x

44. Classwork Do worksheets 8.3 homework page 425 (1-24) Quiz Monday
Test Wednesday

45. Zero Exponent